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THE ROTE-SONG OF THE HOPI 7
steps in the diatonic scale; and of the fourteen possible movements by these intervals down and up from each, ninety-eight in all, sixty-six, or two thirds, will end on other steps of the diatonic scale extended in octaves. If the thirds and sixths employed are subject to the quarter tone aberration common in Pueblo music, the number will be ninety-four, or nineteen twentieths. The diatonic form, either with or without occasional lapses, is the necessary dress of any harmonic melody. In this physico-mathematical fact plainly lies the genesis of the diatonic scale. To argue therefrom to a diatonic consciousness is to mistake cause for effect, the root of the diatonic order for its fruit.
The diatonic form of the present notations by ear is in part the invention of the observer.
The accurate observation of a musical performance of any length is beyond the power of the unaided ear. In the limiting case of Mozart's transcription of singing in Rome, what was carried away was the diatonic form of the rendition, not its accidental material. The fractional tone which Helmholtz reports in the call of certain jiervishes in Cairo impressed a trained ear as a nondescript blunder until after repeated hearings. The invention of the phonograph has given to science a new field of observation, that of music in the making. Fixed on a wax cylinder in reproducible form, the sequence of tone concerned in a performance of music can now be observed and recorded to within minute intervals. This has been attempted in the present phonographic notations, and during the process and later the melodies were wrritten down currently by ear in the customary musical notation. On comparing the two records, the actual (carefully estimated) notes proved in many cases far from the pitch wThich the unaided ear assigned to them and which in general brought them within the bounds of the scale. In liberal measure the diatonic garb which Pueblo singing wears to the European hearer is wroven by his own musical sense. It is a false show due to his inability to divest himself quickly of inveterate prepossessions of the Western ear, or, as we may say, due to the aberration of an instrument unequal to rapid observation.